Transient behavior of full counting statistics in thermal transport

TL;DR

This paper derives a generating function for energy transfer statistics in phononic systems, providing transient cumulant results for a graphene junction and revealing measurement-induced energy flow into the lead.

Contribution

It introduces a novel expression for the generating function of energy counting statistics using contour-ordered self-energy with shifted arguments.

Findings

Transient first four cumulants for a graphene junction.

Measurements induce energy flow into the lead.

New theoretical framework for phononic energy transfer statistics.

Abstract

The generating function of energy counting statistics is derived for phononic junction systems. It is expressed in terms of the contour-ordered self-energy of the lead with shifted arguments, $\Sigma^A(\tau, \tau') = \Sigma_L\bigl(\tau +\hbar x(\tau), \tau' + \hbar x(\tau')\bigr) - \Sigma_L(\tau, \tau')$, where $\Sigma_L(\tau,\tau')$ is the usual contour-ordered self-energy of the left lead. The cumulants of the energy transferred in a given time $t_M$ from the lead to the center is obtained by taking derivatives. A transient result of the first four cumulants of a graphene junction is presented. It is found that measurements cause the energy to flow into the lead.